Finite Group Databasebeta

← #29667616

Subgroups — #29667616

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457146C211yesmaximal, characteristic
2#21456947C211yesmaximal, characteristic, complemented
3#21456846C211yesmaximal, characteristic, complemented
4#21454975C211yesmaximal, characteristic, complemented
5#21445390C211yesmaximal, characteristic, complemented
6#21445383C211yesmaximal, characteristic, complemented
7#21445324C211yesmaximal, characteristic, complemented
8#21445317C211yesmaximal, characteristic, complemented
9#21445266C211yesmaximal, characteristic, complemented
10#21445259C211yesmaximal, characteristic, complemented
11#21445200C211yesmaximal, characteristic, complemented
12#21445193C211yesmaximal, characteristic, complemented
13#21444602C211yesmaximal, characteristic, complemented
14#21444512C211yesmaximal, characteristic, complemented
15C2×C61×#332C211yesmaximal, characteristic, complemented
16#16840312C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840158C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840154—21no—
21#16840130—21no—
22#16840110C2211yescharacteristic
23#16840110C2211yescharacteristic
24#16840080—21no—
25#16840080—21no—
26#16840063—21no—
27#16840058C2211yescharacteristic
28#16840053C2211yescharacteristic
29#16840049—21no—
30#16840049—21no—
31#16839998—21no—
32#16839991—21no—
33#16839978—21no—
34#16839969C2211yescharacteristic
35#16839969C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839964C2211yescharacteristic
38#16839963C2211yescharacteristic
39#16839958C2211yescharacteristic
40#16839918—21no—
41#16839901—21no—
42#16839889C2211yescharacteristic
43#16839886C2211yescharacteristic
44#16839839C2211yescharacteristic
45#16839833—21no—
46#16839827C2211yescharacteristic
47C8×C22⋊D61—21no—
48#16839822—21no—
49#16839819C2211yescharacteristic
50#16839815C2211yescharacteristic
51#16839787—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839505C2211yescharacteristic
59#16839505C2211yescharacteristic
60C2×C4⋊Q8×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×#11758222—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758190—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×D488—21no—
74C2×#11758189—21no—
75C2×C8×D61—21no—
76#14519777C2311yescharacteristic
77#14519774C2311yescharacteristic
78#14519771—21no—
79#14519769D411yescharacteristic
80#14519765—21no—
81#14519765D411yescharacteristic
82#14519760—21no—
83#14519756D411yescharacteristic
84#14519751—21no—
85#14519751—21no—
86#14519751D411yescharacteristic
87C4×Dic122C2311yescharacteristic
88C4×D244—21no—
89C4×D244—21no—
90C4×D244C2311yescharacteristic
91C4×C22⋊D61—21no—
92#14519734—21no—
93#14519711—21no—
94#14519709—21no—
95#14519708—21no—
96#14519708—21no—
97#14519708—21no—
98#14519708—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519701—21no—
107#14519701—21no—
108#14519701—21no—
109#14519701—21no—
110#14519699—21no—
111#14519699—21no—
112#14519699—21no—
113#14519697—21no—
114#14519697—21no—
115#14519697—21no—
116#14519697—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122#14519688—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×Q8×C61—21no—
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61—21no—
131C4⋊Q8×C61—21no—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134C4⋊Q8×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C4⋊C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C22×C4×C61—41no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C2×C22⋊D61—21no—
154C2×C22⋊D61—41no—
155#11758222—82no—
156C2×D244—21no—
157C2×D244—21no—
158C2×D244—21no—
159C2×D244C2×D411yescharacteristic
160C2×C4×D61—21no—
161C2×C4×D61—41no—
162C2×Dic122—21no—
163C2×Dic122C2×D411yescharacteristic
164C2×C8×C61—21no—
165C2×C8×C61—21no—
166C2×C8×C61—21no—
167C2×C8×C61—21no—
168C2×C8×C61—81no—
169C2×C8×C61—81no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C42×C61C2×D411yescharacteristic
177C42×C61C2×D411yescharacteristic
178C42×C61#4111yescharacteristic
179C42×C61C2411yescharacteristic
180C22⋊Dic61—21no—
181#11758202—81no—
182#11758202—81no—
183#11758201—81no—
184#11758201—81no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188#11758198—21no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C2×D411yescharacteristic
194C4⋊Dic61C2×D411yescharacteristic
195#11758196—21no—
196#11758196—21no—
197#11758196—21no—
198#11758196—21no—
199C4×Dic61—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206D488—81no—
207#11758190—81no—
208#11758189—81no—
209C8×D61—81no—
210C23×C61#12111yescharacteristic
211C22×D61—21no—
212C22×D61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—41no—
217Q8×C61—82no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—82no—
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—42no—
233C22⋊D61—82no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—41no—
238D244—21no—
239D244—21no—
240D244—41no—
241D244—41no—
242D244—41no—
243D244—41no—
244D244—81no—
245C4×D61—41no—
246C4×D61—41no—
247C4×D61—82no—
248Dic122—21no—
249Dic122—21no—
250Dic122—81no—
251C8×C61—41no—
252C8×C61—41no—
253C8×C61—41no—
254C8×C61—41no—
255#92418—21no—
256#92418—21no—
257#92418—21no—
258#92418—21no—
259#92418—41no—
260#92418—41no—
261#19589—611nomaximal, Sylow
262C22×C61—21no—
263C22×C61—21no—
264C22×C61#47112yes—
265C22×C61C2×#12111yescharacteristic
266C2×D61—41no—
267C2×D61—41no—
268C2×D61—41no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—21no—
273C4×C61—21no—
274C4×C61—21no—
275C4×C61—21no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#57611yescharacteristic
279C4×C61#57711yescharacteristic
280C4×C61#57711yescharacteristic
281C4×C61#57811yescharacteristic
282Dic61—41no—
283Dic61—41no—
284Dic61—41no—
285Dic61—81no—
286#3247—611no—
287#3227—611no—
288#3218—611no—
289#2994—611no—
290#1702—611no—
291#1701—611no—
292#1692—611no—
293#1691—611no—
294#1682—611no—
295#1681—611no—
296#1672—611no—
297#1671—611no—
298#1573—611no—
299#1551—611no—
300C2×#332D6111yescharacteristic, complemented
301C2×C61—22no—
302C2×C61#304611yescharacteristic
303C2×C61#306211yescharacteristic
304C2×C61C2×#47111yescharacteristic
305D61—81no—
306D61—161no—
307#532—611no—
308C2×C4⋊Q8C2×D6111yescharacteristic
309#529—611no—
310#498—611no—
311#498—611no—
312#497—1221no—
313#491—1221no—
314#486—611no—
315#486—611no—
316#481—1221no—
317#481—1221no—
318#478—1221no—
319#477—611no—
320#476—611no—
321#476—1221no—
322#476—1221no—
323#466—1221no—
324#465—1221no—
325#463—1221no—
326#462—611no—
327#462—611no—
328#461—611no—
329#461—611no—
330#460—611no—
331#459—611no—
332#451—1221no—
333#448—1221no—
334#446—611no—
335C8×Q8—611no—
336#436—611no—
337#435—1221no—
338C8×D4—611no—
339C8×D4—1221no—
340#433—1221no—
341#432—611no—
342#431—611no—
343#424—1221no—
344C2×C4⋊C8C2×D6111yescharacteristic
345C2×C4⋊C8C2×D6111yescharacteristic
346#335—611no—
347#335—611no—
348#334—611no—
349#334—611no—
350#333—611no—
351#333—611no—
352#332C2×D6111yescharacteristic
353#332C2×D6111yescharacteristic
354#332C2×D6111yescharacteristic
355#332C2×D6111yescharacteristic
356#331—611no—
357#331—611no—
358C61#1958911yescharacteristic, complemented, Sylow
359C2×#41—1221no—
360C22×Q8—21no—
361C2×Q16—1221no—
362C2×Q16—1221no—
363C2×SD16—1221no—
364C2×SD16—1221no—
365C2×SD16—1221no—
366C2×D8—1221no—
367C2×M16—1221no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—1221no—
371C4⋊Q8—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—611no—
375C4⋊Q8C22×D6111yescharacteristic
376C4⋊Q8C22×D6111yescharacteristic
377#127—611no—
378#126—1221no—
379#125—611no—
380#124—611no—
381#124—1221no—
382#123—1221no—
383C22⋊Q8—611no—
384#121—611no—
385#121—1221no—
386#121—1221no—
387C4×Q8—611no—
388C4×D4—611no—
389C4×D4—1221no—
390C4×D4—1221no—
391C4×D4—1221no—
392#117—1221no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C42C22×D6111yescharacteristic
396#107—1221no—
397#106—1221no—
398#106—1221no—
399#106—1221no—
400#106—1221no—
401#106—1221no—
402C4⋊C8—21no—
403C4⋊C8—21no—
404C4⋊C8—611no—
405C4⋊C8—611no—
406C4⋊C8—611no—
407C4⋊C8—611no—
408C4⋊C8—1221no—
409C4⋊C8—1221no—
410C4⋊C8C22×D6111yescharacteristic
411C4⋊C8C22×D6111yescharacteristic
412C4⋊C8C22×D6111yescharacteristic
413C4⋊C8C22×D6111yescharacteristic
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103—1221no—
418#103—1221no—
419#102—1221no—
420#102—1221no—
421#102—1221no—
422#102—1221no—
423#102—1221no—
424#102—1221no—
425#102—1221no—
426C22⋊C8—611no—
427C22⋊C8—611no—
428C22⋊C8—1221no—
429C22⋊C8—1221no—
430C22⋊C8—1221no—
431#97—1221no—
432#97—1221no—
433C4×C8—611no—
434C4×C8—611no—
435C4×C8—1221no—
436#41—4882no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—41no—
440C2×Q8—81no—
441C2×Q8—81no—
442C2×Q8—611no—
443C2×Q8—1221no—
444C2×D4—611no—
445C2×D4—1221no—
446C2×D4—1221no—
447C2×D4—1221no—
448C2×D4—1221no—
449C2×D4—2441no—
450C22×C4—41no—
451C22×C4—1221no—
452C22×C4—2441no—
453C22×C4#1175822211yescharacteristic
454C22×C4D4×D6111yescharacteristic
455C22×C4D4×D6111yescharacteristic
456Q16—4881no—
457Q16—4881no—
458SD16—4881no—
459SD16—4881no—
460SD16—4881no—
461D8—4881no—
462M16—4881no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—81no—
468C2×C8—81no—
469C2×C8—611no—
470C2×C8—611no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—1221no—
474C2×C8—1221no—
475C2×C8—4881no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—611no—
483C4⋊C4—611no—
484C4⋊C4—1221no—
485C4⋊C4—1221no—
486C4⋊C4—1221no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C22⋊C4—1221no—
491C22⋊C4—1221no—
492C22⋊C4—1221no—
493C22⋊C4—1221no—
494C22⋊C4—1221no—
495C22⋊C4—2441no—
496C22⋊C4—2441no—
497C42—1221no—
498C42#1175822211yescharacteristic
499C42D4×D6111yescharacteristic
500C42D4×D6111yescharacteristic
501C42C23×D6111yescharacteristic
502C23—1221no—
503C23—2441no—
504C23#1451975011yescharacteristic
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—82no—
510Q8—1221no—
511Q8—1221no—
512Q8—4881no—
513D4—1221no—
514D4—1221no—
515D4—4881no—
516D4—4882no—
517D4—2442no—
518D4—2441no—
519D4—2441no—
520D4—2441no—
521D4—2441no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—4882no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4#1451975011yescharacteristic
538C2×C4#1451975011yescharacteristic
539C2×C4#1451975011yescharacteristic
540C2×C4C2×D4×D6111yescharacteristic
541C2×C4C2×D4×D6111yescharacteristic
542C2×C4C2×#1175822211yescharacteristic
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8—1221no—
548C8—1221no—
549C8—1221no—
550C8—1221no—
551C8—2441no—
552C8—2441no—
553C22—21no—
554C22—21no—
555C22—4881no—
556C22—4881no—
557C22—4881no—
558C22—2441no—
559C22—2441no—
560C22—2441no—
561C22#1684002812yes—
562C22C2×#1451975011yescharacteristic
563C4—21no—
564C4—21no—
565C4—21no—
566C4—21no—
567C4—81no—
568C4—81no—
569C4—4881no—
570C4—2441no—
571C4—2441no—
572C4—2441no—
573C4#1684056311yescharacteristic
574C4#1684056811yescharacteristic
575C4#1684056811yescharacteristic
576C4#1684057511yescharacteristic
577C2—22no—
578C2—9761no—
579C2—4881no—
580C2#2145537411yescharacteristic
581C2#2145549711yescharacteristic
582C2C2×#1684002811yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC22×C61C2×#121
prime radical#21457146C2
hypercenterC2×#332D61
hypocenterC61#19589
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #21456947C2semidirect
3. #21456846C2semidirect
4. #21454975C2semidirect
5. #21445390C2semidirect
6. #21445383C2semidirect
7. #21445324C2semidirect
8. #21445317C2semidirect
9. #21445266C2semidirect
10. #21445259C2semidirect
11. #21445200C2semidirect
12. #21445193C2semidirect
13. #21444602C2semidirect
14. #21444512C2semidirect
15. C2×C61×#332C2semidirect
300. C2×#332D61semidirect
358. C61#19589semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214571462
#214569472
#214568462
#214549752
#214453902
#214453832
#214453242
#214453172
#214452662
#214452592
#214452002
#214451932
#214446022
#214445122
C2×C61×#3322
#1958961